Is there a Haskell equivalent of OOP's abstract classes, using algebraic data types or polymorphism?

In Haskell, is it possible to write a function with a signature that can accept two different (althoug开发者_Python百科h similar) data types, and operate differently depending on what type is passed in?

An example might make my question clearer. If I have a function named myFunction, and two types named MyTypeA and MyTypeB, can I define myFunction so that it can only accept data of type MyTypeA or MyTypeB as its first parameter?

type MyTypeA = (Int, Int, Char, Char)
type MyTypeB = ([Int], [Char])

myFunction :: MyTypeA_or_MyTypeB -> Char
myFunction constrainedToTypeA = something
myFunction constrainedToTypeB = somethingElse

In an OOP language, you could write what I'm trying to achieve like so:

public abstract class ConstrainedType {
}

public class MyTypeA extends ConstrainedType {
    ...various members...
}

public class MyTypeB extends ConstrainedType {
    ...various members...
}

...

public Char myFunction(ConstrainedType a) {
    if (a TypeOf MyTypeA) {
        return doStuffA();
    }
    else if (a TypeOf MyTypeB) {
        return doStuffB();
    }
}

I've been reading about algebraic data types and I think I need to define a Haskell type, but I'm not sure how to go about defining it so that it can store one type or another, and also how I use it in my own functions.

Yes, you are correct, you are looking for algebraic data types. There is a great tutorial on them at Learn You a Haskell.

For the record, the concept of an abstract class from OOP actually has three different translations into Haskell, and ADTs are just one. Here is a quick overview of the techniques.

Algebraic Data Types

Algebraic data types encode the pattern of an abstract class whose subclasses are known, and where functions check which particular instance the object is a member of by down-casting.

abstract class IntBox { }

class Empty : IntBox { }

class Full : IntBox {
    int inside;
    Full(int inside) { this.inside = inside; }
}

int Get(IntBox a) {
    if (a is Empty) { return 0; }
    if (a is Full)  { return ((Full)a).inside; }
    error("IntBox not of expected type");
}

Translates into:

data IntBox = Empty | Full Int

get :: IntBox -> Int
get Empty = 0
get (Full x) = x

Record of functions

This style does not allow down-casting, so the Get function above would not be expressible in this style. So here is something completely different.

abstract class Animal { 
    abstract string CatchPhrase();
    virtual void Speak() { print(CatchPhrase()); }
}

class Cat : Animal {
    override string CatchPhrase() { return "Meow"; }
}

class Dog : Animal {
    override string CatchPhrase() { return "Woof"; }
    override void Speak() { print("Rowwrlrw"); }
}

Its translation in Haskell doesn't map types into types. Animal is the only type, and Dog and Cat are squashed away into their constructor functions:

data Animal = Animal {
    catchPhrase :: String,
    speak       :: IO ()
}

protoAnimal :: Animal
protoAnimal = Animal {
    speak = putStrLn (catchPhrase protoAnimal)
}

cat :: Animal
cat = protoAnimal { catchPhrase = "Meow" }

dog :: Animal
dog = protoAnimal { catchPhrase = "Woof", speak = putStrLn "Rowwrlrw" }

There are a few different permutations of this basic concept. The invariant is that the abstract type is a record type where the methods are the fields of the record.

EDIT: There is a good discussion in the comments on some of the subtleties of this approach, including a bug in the above code.

Typeclasses

This is my least favorite encoding of OO ideas. It is comfortable to OO programmers because it uses familiar words and maps types to types. But the record of functions approach above tends to be easier to work with when things get complicated.

I'll encode the Animal example again:

class Animal a where
    catchPhrase :: a -> String
    speak       :: a -> IO ()

    speak a = putStrLn (catchPhrase a)

data Cat = Cat 
instance Animal Cat where
    catchPhrase Cat = "Meow"

data Dog = Dog
instance Animal Dog where
    catchPhrase Dog = "Woof"
    speak Dog = putStrLn "Rowwrlrw"

This looks nice, doesn't it? The difficulty comes when you realize that even though it looks like OO, it doesn't really work like OO. You might want to have a list of Animals, but the best you can do right now is Animal a => [a], a list of homogeneous animals, eg. a list of only Cats or only Dogs. Then you need to make this wrapper type:

{-# LANGUAGE ExistentialQuantification #-}

data AnyAnimal = forall a. Animal a => AnyAnimal a
instance Animal AnyAnimal where
    catchPhrase (AnyAnimal a) = catchPhrase a
    speak (AnyAnimal a) = speak a

And then [AnyAnimal] is what you want for your list of animals. However, it turns out that AnyAnimal exposes exactly the same information about itself as the Animal record in the second example, we've just gone about it in a roundabout way. Thus why I don't consider typeclasses to be a very good encoding of OO.

And thus concludes this week's edition of Way Too Much Information!

It sounds like you might want to read up on typeclasses.

Consider this example using TypeClasses.

We define a c++-like "abstract class" MVC based on three types (note MultiParamTypeClasses): tState tAction tReaction in order to define a key function tState -> tAction -> (tState, tReaction) (when an action is applied to the state, you get a new state and a reaction.

The typeclass has three "c++ abstract" functions, and some more defined on the "abstract" ones. The "abstract" functions will be defined when and instance MVC is needed.

{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, NoMonomorphismRestriction #-}


-- -------------------------------------------------------------------------------

class MVC tState tAction tReaction | tState -> tAction tReaction where
      changeState :: tState -> tAction -> tState       -- get a new state given the current state and an action ("abstract")
      whatReaction :: tState -> tReaction              -- get the reaction given a new state ("abstract")
      view :: (tState, tReaction) -> IO ()             -- show a state and reaction pair ("abstract")

      -- get a new state and a reaction given an state and an action (defined using previous functions)
      runModel :: tState -> tAction -> (tState, tReaction) 
      runModel s a = let
                                ns = (changeState s a) 
                                r = (whatReaction ns) 
                  in (ns, r)

      -- get a new state given the current state and an action, calling 'view' in the middle (defined using previous functions)
      run :: tState -> tAction -> IO tState
      run s a = do
                        let (s', r) = runModel s a
                        view (s', r)
                        return s'

      -- get a new state given the current state and a function 'getAction' that provides actions from "the user" (defined using previous functions)
      control :: tState -> IO (Maybe tAction) -> IO tState
      control s getAction = do
              ma <- getAction
              case ma of
                   Nothing -> return s
                   Just a -> do
                              ns <- run s a
                              control ns getAction


-- -------------------------------------------------------------------------------

-- concrete instance for MVC, where
-- tState=Int tAction=Char ('u' 'd') tReaction=Char ('z' 'p' 'n')
-- Define here the "abstract" functions
instance MVC Int Char Char where
         changeState i c 
                     | c == 'u' = i+1 -- up: add 1 to state
                     | c == 'd' = i-1 -- down: add -1 to state
                     | otherwise = i -- no change in state

         whatReaction i
                      | i == 0 = 'z' -- reaction is zero if state is 0
                      | i < 0 = 'n' -- reaction is negative if state < 0                     
                      | otherwise = 'p' -- reaction is positive if state > 0

         view (s, r) = do
                  putStrLn $ "view: state=" ++ (show s) ++ " reaction=" ++ (show r) ++ "\n"

--

-- define here the function "asking the user"
getAChar :: IO (Maybe Char) -- return (Just a char) or Nothing when 'x' (exit) is typed
getAChar = do
         putStrLn "?"
         str <- getLine
         putStrLn ""
         let c = str !! 0
         case c of
              'x' -> return Nothing
              _ -> return (Just c)


-- --------------------------------------------------------------------------------------------
-- --------------------------------------------------------------------------------------------

-- call 'control' giving the initial state and the "input from the user" function 
finalState = control 0 getAChar :: IO Int

-- 

main = do
     s <- finalState
     print s